Question: Rewrite as a simplified fraction. ${2.\overline{75} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 275.7575...\\ 1x &= 2.7575...\end{align*}}$ Subtracting the two equations, we have: ${99x = 273}$ ${x = \dfrac{273}{99}} $ ${x = \dfrac{91}{33}} \text{or} {2 \dfrac{25}{33}}$